TSTP Solution File: SET930+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:40:44 EDT 2024
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 7 unt; 0 def)
% Number of atoms : 105 ( 46 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 129 ( 58 ~; 37 |; 29 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 58 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ~ in(A,C)
& ( in(B,C)
| A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(A,C)
& ~ in(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(A,C)
& in(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B,C] :
~ ( set_difference(unordered_pair(A,B),C) != empty_set
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B,C] :
~ ( set_difference(unordered_pair(A,B),C) != empty_set
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f15,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) != singleton(A)
| ( ~ in(A,C)
& ( in(B,C)
| A = B ) ) )
& ( set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C)
| ( ~ in(B,C)
& A != B ) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f16,plain,
( ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != singleton(A)
| ( ~ in(A,C)
& ( in(B,C)
| A = B ) ) )
& ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C)
| ( ~ in(B,C)
& A != B ) ) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f19,plain,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| in(X0,X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f25,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
| ( ~ in(A,C)
& ~ in(B,C) ) )
& ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
| in(A,C)
| in(B,C) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f26,plain,
( ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
| ( ~ in(A,C)
& ~ in(B,C) ) )
& ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
| in(A,C)
| in(B,C) ) ),
inference(miniscoping,[status(esa)],[f25]) ).
fof(f29,plain,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
| in(X0,X2)
| in(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f30,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) != empty_set
| ( in(A,C)
& in(B,C) ) )
& ( set_difference(unordered_pair(A,B),C) = empty_set
| ~ in(A,C)
| ~ in(B,C) ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f31,plain,
( ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != empty_set
| ( in(A,C)
& in(B,C) ) )
& ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
| ~ in(A,C)
| ~ in(B,C) ) ),
inference(miniscoping,[status(esa)],[f30]) ).
fof(f34,plain,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = empty_set
| ~ in(X0,X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f35,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) != empty_set
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f36,plain,
( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != empty_set
& set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != singleton(sk0_2)
& set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != singleton(sk0_3)
& set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != unordered_pair(sk0_2,sk0_3) ),
inference(skolemization,[status(esa)],[f35]) ).
fof(f37,plain,
set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != empty_set,
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != singleton(sk0_2),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f39,plain,
set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != singleton(sk0_3),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f40,plain,
set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != unordered_pair(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f58,plain,
( spl0_0
<=> in(sk0_2,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f61,plain,
( spl0_1
<=> in(sk0_3,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f64,plain,
( in(sk0_2,sk0_4)
| ~ in(sk0_3,sk0_4) ),
inference(resolution,[status(thm)],[f19,f38]) ).
fof(f65,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f64,f58,f61]) ).
fof(f66,plain,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X1)
| in(X1,X2)
| ~ in(X0,X2) ),
inference(paramodulation,[status(thm)],[f13,f19]) ).
fof(f76,plain,
( ~ in(sk0_2,sk0_4)
| ~ in(sk0_3,sk0_4) ),
inference(resolution,[status(thm)],[f34,f37]) ).
fof(f77,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f76,f58,f61]) ).
fof(f80,plain,
( in(sk0_3,sk0_4)
| ~ in(sk0_2,sk0_4) ),
inference(resolution,[status(thm)],[f66,f39]) ).
fof(f81,plain,
( spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f80,f61,f58]) ).
fof(f84,plain,
( in(sk0_2,sk0_4)
| in(sk0_3,sk0_4) ),
inference(resolution,[status(thm)],[f29,f40]) ).
fof(f85,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f84,f58,f61]) ).
fof(f120,plain,
$false,
inference(sat_refutation,[status(thm)],[f65,f77,f81,f85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 29 21:46:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.6.0
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.37 % Elapsed time: 0.020502 seconds
% 0.12/0.37 % CPU time: 0.029516 seconds
% 0.12/0.37 % Total memory used: 12.874 MB
% 0.12/0.37 % Net memory used: 12.805 MB
%------------------------------------------------------------------------------